Homogenization for the cubic nonlinear Schrödinger equation on ${\mathbb{R}}^2$

Abstract

We study the defocusing inhomogeneous mass-critical nonlinear Schrödinger equation on ${\mathbb{R}}^2$ $$i{u}_t+\Delta u=g(nx)|u{|}^{2}u$$ for initial data in $L^2({\mathbb{R}}^2)$. We obtain sufficient conditions on $g$ to ensure existence and uniqueness of global solutions for $n$ sufficiently large, as well as homogenization.

25 pages